Abstract
This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.
| Original language | English |
|---|---|
| Pages (from-to) | 485-497 |
| Number of pages | 13 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 40 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2007 May |
Keywords
- Circumstance process
- Discounted aggregate claims
- Laplace-Stieltjes transform
- Moments
ASJC Scopus subject areas
- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty
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Cite this
Kim, B., & Kim, H. S. (2007). Moments of claims in a Markovian environment. Insurance: Mathematics and Economics, 40(3), 485-497. https://doi.org/10.1016/j.insmatheco.2006.07.004